Can't see anywhere where to reset security questions or two-step verification.

It's one or the other - you can't have both.

If you have 2-step verification enabled, you can turn it off:

http://support.apple.com/kb/HT5631

If you don't have it enabled but have Security questions set, go to http://appleid.apple.com and click Password & security in the sidebar. You will be able to change your questions (you will need to answer two of the originals to get into this).

Did you enable two-step verification in the first place? As I say it's either that or security questions, you can't have both, so are we talking about verification or security questions?

If you go to http://appleid.apple.com and sign in, do you see the 'Password and Security' link in the sidebar? What exactly happens when you click it?

OK: you have not set up two-step verification (or you wouldn't be presented with the questions).

If you don't know the answers and you don't have a link to send the answer to a specified address (shown partially) you will have to contact Support:

Go to https://getsupport.apple.com ; click 'See all products and services', then 'More Products and Services, then 'Apple ID', then 'Other Apple ID Topics' then 'Forgotten Apple ID security questions'.